Question

An item costs $9000 today. What will the item cost in 10 years assuming an inflation rate of 4.1% compounded continuously? The item will cost: less than $13,460 between $13,460 and $13,500 between $13,500 and $13,540 between $13,540 and $13,580 more than $13,580

Answer 1

Main answer: The item will cost more than $13,580 in 10 years assuming an inflation rate of 4.1% compounded continuously.

To calculate the future cost of the item, we can use the continuous compound interest formula:

A = P * e^(rt)

Where:
A is the future cost of the item
P is the present cost of the item ($9000)
e is the mathematical constant approximately equal to 2.71828
r is the inflation rate (4.1% or 0.041)
t is the time period in years (10 years)

Plugging in the values, we have:

A = 9000 * e^(0.041 * 10)

Using a calculator, we find that e^(0.041 * 10) is approximately 1.4922. Multiplying this by $9000, we get:

A ≈ 9000 * 1.4922 ≈ $13,429.80

Therefore, the item will cost more than $13,580 in 10 years assuming an inflation rate of 4.1% compounded continuously.

Answer in 100 words: The item will cost more than $13,580 in 10 years assuming a continuous compounding inflation rate of 4.1%. To calculate the future cost, we use the continuous compound interest formula A = P * e^(rt). Plugging in the values, we have A = 9000 * e^(0.041 * 10). Using a calculator, we find that e^(0.041 * 10) is approximately 1.4922. Multiplying this by $9000, we get A ≈ 9000 * 1.4922 ≈ $13,429.80. Therefore, the item will cost more than $13,580 in 10 years assuming an inflation rate of 4.1% compounded continuously.

Conclusion: The item will cost more than $13,580 in 10 years assuming an inflation rate of 4.1% compounded continuously.